
For brevity we shall write \(H(\operatorname{grad})= H(\operatorname{grad}, \Omega )\)  etc. where there is no potential confusion.
Our problems of interest (REF )-()
often arise as subproblems in the construction of fast
preconditioners for more complex systems involving solution variables in (REF )-() [1]}, [2]},
and are the canonical maps for transforming derivatives to gradients in optimization problems posed in these spaces [3]}.
